Enforcing k-space data consistency in deep learning-based CS reconstruction is straightforward and time-efficient for Cartesian trajectories, which only needs forward and inverse Fourier transforms between k-space and image space. However, for non-Cartesian trajectories, the non-Cartesian k-space needs to be gridded onto a Cartesian basis. Gridding is time-consuming and typically needs to be performed for each iteration of the network training and testing, which slows down the process profoundly and offsets the deep learning advantage of fast inference [1]}. For this reason, a previous study employed a light convolutional neural network (CNN) component with very few parameters and implemented a pretraining and fine-tuning strategy to train a radial reconstruction network [1]}, imposing limits on the application and performance of deep networks. Other work either used image-to-image networks [3]}, [4]}, [5]}, [6]}, [7]}, [8]} or gridded the radial k-space before the network training [9]}, [10]}, [11]}. For image-to-image networks, the network generated images may lack k-space data consistency and therefore lose image fidelity [1]}. Gridding non-Cartesian k-space before the network training can avoid the repeated gridding problem. However, the network cannot learn to compensate for the gridding error [13]}. In addition, the undersampling artifacts in radial trajectory are global streaking artifacts which are hard to remove in the image domain with local convolution kernels.
